President Obama's push to raise the federal minimum wage to $10.10 an hour, coupled with recent state-level increases, is welcome news for many people getting by on small paychecks.

That's because a crazy patchwork of rules and exemptions lets employers pay some kinds of workers below the full minimum wage -- in some cases, well below.

The rules are complex at the federal and state levels. But here's a partial list of how they treat certain classes of workers.

Disabled workers: Under federal law, employers may apply for a special certificate to pay less than the minimum wage to anyone "whose earning or productive capacity is impaired by a physical or mental disability, including those relating to age or injury."

The rule was established in 1938 and has hardly changed since. It was originally intended to encourage businesses to hire veterans with disabilities in an industrial economy, according to the National Disability Rights Network.

But today it's used primarily to employ disabled people in what are called sheltered workshops that often involve some form of manual labor -- such as packing boxes, doing laundry or printing t-shirts.

An estimated 400,000 disabled people hold such jobs. And their hourly pay is based on the employer's assessment of their productivity relative to the productivity of non-disabled workers.

Anyone working for very small businesses: Under federal law, an employer doesn't have to pay the minimum wage to a worker if the company's annual gross sales are less than $500,000 and if it doesn't do any business across state lines, according to Tsedeye Gebreselassie, a staff attorney at the National Employment Law Project.

Teenage trainees: Federal law allows employers to pay $4.25 an hour -- $3 less than the current federal minimum -- to anyone under 20 for the first 90 days of employment, according to the Congressional Research Service.

Maryland, which just increased its state minimum wage to $10.10, now exempts those under 20 for the first 180 days, during which employers are allowed to pay them 15% less than the state minimum.

Federal law also lets employers pay 85% of the federal minimum (or $6.16/hour) to full-time students working in retail or service businesses, in an agricultural occupation, or at an institute of higher education.

They are also allowed to pay just 75% of the minimum wage (or $5.44/hour) to students who are employed part-time as part of a vocational training program at an accredited school.

Tipped workers: Currently, under federal law, employers only need to pay tipped workers a minimum wage of $2.13 an hour -- if that wage plus the tips push the worker's pay to at least the $7.25 federal minimum.

But those who advocate for higher wages for tipped workers say that provision is very hard to enforce with employers.

A bill that the Senate is likely to consider next week would raise the federal minimum to $10.10 and also gradually raise the $2.13 minimum for tipped workers to 70% of the federal minimum.

Among states, there's a hodgepodge of rules.

The road to a minimum wage

Seven states require employers to pay tipped workers the state's full minimum on top of any tips those workers receive, according to NELP.

In at least 24 other states, companies must pay tipped workers a subminimum wage that is higher than the $2.13 required at the federal level.

But even where that's the case, there can be wrinkles. For instance, even though Maryland increased its state minimum wage,it did not raise tipped workers' base hourly wage of $3.63. Instead it chose to freeze it at that level.

That's a step back, according to the Economic Policy Institute's David Cooper. Why? Because previously, Maryland had mandated that tipped workers' base wage be set at 50% of the state minimum, which is now set to gradually increase to $10.10 from $7.25.

Some agricultural employees: Workers who are immediate relatives of an agricultural employer do not have minimum wage protection at the federal level, nor do some other agricultural workers with certain hours and job duty requirements.

Practically, this exemption usually applies onlyto very small family farms. The vast majority of farm workers are covered under minimum wage laws, NELP's Gebreselassie said.

Home care aides: Until now, home care workers who are hired primarily to dress, feed, bathe and otherwise attend to an infirm person's daily needs at home typically haven't received federal minimum wage protection.

But that will change on Jan. 1, 2015. Under a new set of rules governing "companionship services," home care agencies must pay such aides at least the full minimum wage. If the aide is employed solely by a private household, they may still be exempt from minimum wage protection but only if their primary duties fall within a much narrower definition of companion services.

Other exempt workers: Other groups exempt from federal minimum wage protection include newspaper delivery people, occasional babysitters, employees of small circulation newspapers, those elected to state and local government offices (and their staffs); and anyone who works for some seasonal businesses such as amusement parks and summer camps.